91Ó°ÊÓ

For the following exercises, find the multiplicative inverse of each matrix, if it exists. $$\left[\begin{array}{rr}-2 & 2 \\ 3 & 1\end{array}\right]$$

For the following exercises, solve each system by substitution. $$ \begin{aligned} 4 x-3 y+5 z &=31 \\\\-x+2 y+4 z &=20 \\ x+5 y-2 z &=-29 \end{aligned} $$

Write the linear system from the augmented matrix. \(\left[\begin{array}{rrr|r}8 & 29 & 1 & 43 \\ -1 & 7 & 5 & 38 \\ 0 & 0 & 3 & 10\end{array}\right]\)

For the following exercises, solve the system of nonlinear equations using elimination. $$\begin{aligned} y^{2}-x^{2} &=9 \\ 3 x^{2}+2 y^{2} &=8 \end{aligned}$$

Solve each system by substitution. $$ \begin{aligned} 4 x-3 y+5 z &=31 \\ -x+2 y+4 z &=20 \\ x+5 y-2 z &=-29 \end{aligned} $$

For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. $$\frac{10 x}{x^{2}-25}$$

For the following exercises, find the determinant. \(\begin{array}{rr}-1.1 & 0.6 \\ 7.2 & -0.5\end{array} \mid\)

For the following exercises, solve the system of nonlinear equations using elimination. $$\begin{aligned} x^{2}+y^{2}+\frac{1}{16} &=2500 \\ y &=2 x^{2} \end{aligned}$$

Solve the system of nonlinear equations using elimination. $$ \begin{aligned} x^{2}+y^{2}+\frac{1}{16} &=2500 \\ y &=2 x^{2} \end{aligned} $$

Solve each system by substitution. $$ \begin{aligned} 5 x-2 y+3 z &=4 \\ -4 x+6 y-7 z &=-1 \\ 3 x+2 y-z &=4 \end{aligned} $$